Mathematical statements used by mathematicians are usually provable. In other words, the mathematical statement: "volume of a sphere = (4/3)πr3" (where r is the radius of the sphere), has a mathematical proof.

(a)What is a mathematical statement?
(b) What is a mathematical proof?
(c) Explain the truth of A implies B(d) What is a truth table?
(e) Suppose X makes the following statement to Y: "If it is hot (above 80o F), Maybelline goes braless." What scenario in the illustrated truth table presents X as a liar?

The strings:
S7P2A21 (Identity - Physical Property).

The math:
Pj Problem of Interest is of type identity (physical property). Determining truth is an identity problem.

(a) A mathematical statement is an expression that is either true or false. For example, 0 = 0 and 1 = 0 are both mathematical statements. The former is true while the latter is false. The expression 3n + 2 is not a mathematical statement.

(b) A mathematical proof is a group of truthful mathematical statements that as a whole convincingly establish the truth of a given mathematical statement. For example, the group of mathematical statements that establish that the area of a circle is πr2 is the mathematical proof of the area of a circle.

(c) Given two statements A (the hypothesis) and B (the conclusion) each of which may be either true or false, the truth of A implies B means it is true that if A is true then B is true.

(d) A truth table is a presentation of the possible truth values of the individual statements of a complex statement in order to determine when the complex statement is true

(e) Suppose A is the statement :"when it is hot"
B is the statement:"Maybelline goes braless"
X is presented as a liar if it is hot and Maybelline does not goe braless. In other words, A is true but B is false. So, A implies B is false. Second row of truth table.